Problem: Express this quotient in scientific notation: ${\frac{3.640\times 10^{5}} {4.0\times 10^{1}}}$
Answer: Start by collecting like terms together. $= {\frac{3.640} {4.0}} \times{\frac{10^{5}} {10^{1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.91 \times 10^{5\,-\,1}$ $= 0.91 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.91$ is the same as $9.10 \div 10$ , or $9.10 \times 10^{-1}$ $ = {9.10 \times 10^{-1}} \times 10^{4} $ $= 9.10\times 10^{3}$